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The aim of this paper is to generalize the convexity preserving properties of sets by direct and inverse images initially stated for set-valued ratios of affine functions to a broader class of fractional type set-valued functions which strictly includes the first one.

Based on multiple experimental researches the paper presents graphics and mathematical models obtained by data processing using modern software of wear dependence and cumulate thermal deformations according to the number of controlled number of pieces and dimension of the gauge. Taking into consideration the obtained results, the paper presents conclusions and recommendations over these factors of influence (wear and thermal deformation) over the accuracy quality control of the products, recommendations design and optimal usage of shaft gauges.